Perturbation techniques in irregular spline-type spaces

In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue...

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Autores principales: Feichtinger, H.G., Molter, U., Romero, J.L.
Formato: JOUR
Materias:
Irregular sampling
Nonuniform sampling
Perturbation
Sampling
Spline-type spaces
Estimation
Set theory
Perturbation techniques
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_02196913_v6_n2_p249_Feichtinger
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spelling todo:paper_02196913_v6_n2_p249_Feichtinger2023-10-03T15:11:09Z Perturbation techniques in irregular spline-type spaces Feichtinger, H.G. Molter, U. Romero, J.L. Irregular sampling Nonuniform sampling Perturbation Sampling Spline-type spaces Estimation Sampling Set theory Irregular sampling Nonuniform sampling Spline-type spaces Perturbation techniques In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue in the spirit of Kadec's Theorem for bandlimited functions (see Refs. 14 and 15). We further derive some quantitative estimates on the amount by which a sampling set can be perturbed, and finally prove a result on the existence of optimal perturbations (with the stability of reconstruction being the optimality criterion). Finally, the techniques developed in the earlier parts of the paper are used to study the problem of disturbing a basis for a spline-type space, in order to derive a sufficient criterion for a space generated by irregular translations to be a spline-type space. © 2008 World Scientific Publishing Company. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Romero, J.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Irregular sampling
Nonuniform sampling
Perturbation
Sampling
Spline-type spaces
Estimation
Sampling
Set theory
Irregular sampling
Nonuniform sampling
Spline-type spaces
Perturbation techniques
spellingShingle Irregular sampling
Nonuniform sampling
Perturbation
Sampling
Spline-type spaces
Estimation
Sampling
Set theory
Irregular sampling
Nonuniform sampling
Spline-type spaces
Perturbation techniques
Feichtinger, H.G.
Molter, U.
Romero, J.L.
Perturbation techniques in irregular spline-type spaces
topic_facet Irregular sampling
Nonuniform sampling
Perturbation
Sampling
Spline-type spaces
Estimation
Sampling
Set theory
Irregular sampling
Nonuniform sampling
Spline-type spaces
Perturbation techniques
description In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue in the spirit of Kadec's Theorem for bandlimited functions (see Refs. 14 and 15). We further derive some quantitative estimates on the amount by which a sampling set can be perturbed, and finally prove a result on the existence of optimal perturbations (with the stability of reconstruction being the optimality criterion). Finally, the techniques developed in the earlier parts of the paper are used to study the problem of disturbing a basis for a spline-type space, in order to derive a sufficient criterion for a space generated by irregular translations to be a spline-type space. © 2008 World Scientific Publishing Company.
format JOUR
author Feichtinger, H.G.
Molter, U.
Romero, J.L.
author_facet Feichtinger, H.G.
Molter, U.
Romero, J.L.
author_sort Feichtinger, H.G.
title Perturbation techniques in irregular spline-type spaces
title_short Perturbation techniques in irregular spline-type spaces
title_full Perturbation techniques in irregular spline-type spaces
title_fullStr Perturbation techniques in irregular spline-type spaces
title_full_unstemmed Perturbation techniques in irregular spline-type spaces
title_sort perturbation techniques in irregular spline-type spaces
url http://hdl.handle.net/20.500.12110/paper_02196913_v6_n2_p249_Feichtinger
work_keys_str_mv AT feichtingerhg perturbationtechniquesinirregularsplinetypespaces
AT molteru perturbationtechniquesinirregularsplinetypespaces
AT romerojl perturbationtechniquesinirregularsplinetypespaces
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